theorem Th4:
  n divides m & k divides m & n,k are_coprime implies (n*k) divides m
proof
  assume that
A1: n divides m and
A2: k divides m & n,k are_coprime;
  consider t1 be Nat such that
A3: m = n*t1 by A1,NAT_D:def 3;
  k divides t1 by A2,A3,Th3;
  then consider t2 be Nat such that
A4: t1 = k*t2 by NAT_D:def 3;
  m = (n*k)*t2 by A3,A4;
  hence thesis;
end;
